Exploiting Low-Rank Structure in Genomic Relationship Matrices for Computationally Efficient Optimum Contribution Selection
- 1Skogforsk Savar
Abstract
Motivation: Optimum contribution selection (OCS) maximizes genetic gain under a constraint on relatedness. Genomic relationship matrices are dense, so the quadratic term costs O(n^3) operations, and existing OCS software assumes pedigree sparsity. Results: We replace the relationship matrix by its leading eigenpairs, computed by randomized SVD, and solve OCS in factorized form. On Norway spruce population (n=5,525), ranks 10--30 kept the exact objective within 1% of the optimum at 110--330-fold speedups; on the QTL-MAS 2010 (n=3,226), ranks up to 100 were needed (24-211 fold). The required rank rises as the diversity constraint loosens. Gain alone is a misleading accuracy check, since coancestry exceeded the optimum by up to 28%, so we choose the rank on the exact objective, which can be checked without a dense solve. The speedup comes from computing only the leading eigenpairs. We extend the factorization to robust OCS (18-fold). Availability and implementation: Julia implementation, and examples are available at https://github.com/jonhar97/fastocs under the MIT license (archived at Zenodo, DOI 10.5281/zenodo.23214804).
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BibTeX
@misc{ahlinder2026exploiting,
title = {{Exploiting Low-Rank Structure in Genomic Relationship Matrices for Computationally Efficient Optimum Contribution Selection}},
author = {J. Ahlinder and P. Waldmann},
howpublished = {bioRxiv},
year = {2026},
month = oct,
doi = {10.64898/2026.10.07.757325},
url = {https://www.biorxiv.org/content/10.64898/2026.10.07.757325v1},
note = {CC BY-NC},
}
RIS
TY - UNPB
TI - Exploiting Low-Rank Structure in Genomic Relationship Matrices for Computationally Efficient Optimum Contribution Selection
AU - J. Ahlinder
AU - P. Waldmann
PY - 2026
DA - 2026/10/07
PB - bioRxiv
DO - 10.64898/2026.10.07.757325
UR - https://www.biorxiv.org/content/10.64898/2026.10.07.757325v1
AB - Motivation: Optimum contribution selection (OCS) maximizes genetic gain under a constraint on relatedness. Genomic relationship matrices are dense, so the quadratic term costs O(n^3) operations, and existing OCS software assumes pedigree sparsity. Results: We replace the relationship matrix by its leading eigenpairs, computed by randomized SVD, and solve OCS in factorized form. On Norway spruce population (n=5,525), ranks 10--30 kept the exact objective within 1% of the optimum at 110--330-fold speedups; on the QTL-MAS 2010 (n=3,226), ranks up to 100 were needed (24-211 fold). The required rank rises as the diversity constraint loosens. Gain alone is a misleading accuracy check, since coancestry exceeded the optimum by up to 28%, so we choose the rank on the exact objective, which can be checked without a dense solve. The speedup comes from computing only the leading eigenpairs. We extend the factorization to robust OCS (18-fold). Availability and implementation: Julia implementation, and examples are available at https://github.com/jonhar97/fastocs under the MIT license (archived at Zenodo, DOI 10.5281/zenodo.23214804).
ER -